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Linear Algebra

Syllabus

Table of contents

  1. Overview
  2. Policies
    1. Cheating
    2. Homework
    3. Final Exam
    4. Grades
  3. Resources

Overview

In this course, our aim is to explain this beautiful and useful part of mathematics. We’ ll start with solving linear equations $A\mathbf{x}=\mathbf{b}$. The vector of $A\mathbf{x}$ is a linear combination of the columns of $A$. By solving the equations, We’ll introduce the four fundamental subspaces for the matrix $A$. Then we’ll explain the fundamental theorem of linear algebra. Also we’ll show some applications.

By the end of the course, students will learn:

  • The row and column picture of $A\mathbf{x}=\mathbf{b}$, and hence the elimination in the beautiful form $A=LU$.
  • The concept of subspace and the four fundamental subspaces for the matrix $A$.
  • Determinants.
  • Eigenvalues and eigenvectors.
  • Linear transformations.
  • Singular value decomposition.(SVD)
  • Applications of linear algebra.

Policies

Cheating

You are encouraged to collaborate with your classmates or utilize online resources for any homework. Actually, you can also ask for the instructor. However, directly copying and pasting code or answers is prohibited. If I ask you how you proved or why your answers are correct and you do not know, it will be evident that you have copied it. Don’t take the risk.

Homework

The HW will be released once a week.

Please note that late submissions will incur a 25% penalty.

Final Exam

This course will have only one exam, the final exam. The more information will be decided later.

Grades

Students’ gradesGrade will be determined by the following two components:

  • HomeworkHW,
  • Final ExamExam,
The final grade will be calculated using the following equation:

Grade = 40%* HW + 60%* Exam

Resources

This course website, Linear Algebra, will be your one-stop resource for the syllabus, schedule and homework links.

Reference

Here’re some recommended books：

Some online resources: